COMS W3261
Computer Science Theory
Lecture 14: November 7, 2012
Algorithms and the Church-Turing Thesis

Outline

1. Definition of Algorithm

2. Programming techniques for Turing machines

3. Variants of Turing machines

4. The Church-Turing Thesis

5. The Diagonalization Language Ld is not Recursively Enumerable

6. Reading Assignment

7. Practice Problems

  1. Informally describe how a single-tape Turing machine can simulate a two-tape Turing machine.
  2. Informally describe how a deterministic Turing machine can simulate a nondeterministic Turing machine.
  3. Informally describe how a pushdown automaton with two stacks can simulate a Turing machine.
  4. Given a suitable encoding of input strings and Turing machines, show that L = { wi | wi is not accepted by M2i } is not recursively enumerable.

aho@cs.columbia.edu